Design of Far Field Beamforming Problem by Window Function

The design of the broadband beamformer problem is to find the coefficients vector for all FIR filters such that output fits to a given target spatial directivity pattern in a specified domain. This problem is always very complicated. In this paper, a fast window function method is proposed to solve this problem. First, a simplified optimization problem is formulated, where the frequency response function is the decision function. Then an optimal frequency response vector can be obtained by solving this problem. Next the window function is applied to cut off the infinite length of the coefficient. The window function method is efficient and can be applied in real time applications. Numerical example is illustrated to show the efficiency of the method.